Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2

Percentage Accurate: 99.8% → 99.9%

Time: 12.2s

Alternatives: 11

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ (- x (* (+ y 0.5) (log y))) y) z))

C

double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * log(y))) + y) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x - ((y + 0.5d0) * log(y))) + y) - z
end function

Java

public static double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * Math.log(y))) + y) - z;
}

Python

def code(x, y, z):
	return ((x - ((y + 0.5) * math.log(y))) + y) - z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x - Float64(Float64(y + 0.5) * log(y))) + y) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x - ((y + 0.5) * log(y))) + y) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - N[(N[(y + 0.5), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision] - z), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ (- x (* (+ y 0.5) (log y))) y) z))

C

double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * log(y))) + y) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x - ((y + 0.5d0) * log(y))) + y) - z
end function

Java

public static double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * Math.log(y))) + y) - z;
}

Python

def code(x, y, z):
	return ((x - ((y + 0.5) * math.log(y))) + y) - z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x - Float64(Float64(y + 0.5) * log(y))) + y) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x - ((y + 0.5) * log(y))) + y) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - N[(N[(y + 0.5), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision] - z), $MachinePrecision]

Alternative 1: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ x + \left(\mathsf{fma}\left(\log y, -0.5 - y, y\right) - z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (- (fma (log y) (- -0.5 y) y) z)))

C

double code(double x, double y, double z) {
	return x + (fma(log(y), (-0.5 - y), y) - z);
}

Julia

function code(x, y, z)
	return Float64(x + Float64(fma(log(y), Float64(-0.5 - y), y) - z))
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[Log[y], $MachinePrecision] * N[(-0.5 - y), $MachinePrecision] + y), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
2. Step-by-step derivation

   1. associate--l+ 99.8%

      \[\leadsto \color{blue}{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)} \]

   2. sub-neg 99.8%

      \[\leadsto \color{blue}{\left(x + \left(-\left(y + 0.5\right) \cdot \log y\right)\right)} + \left(y - z\right) \]

   3. associate-+l+ 99.8%

      \[\leadsto \color{blue}{x + \left(\left(-\left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)\right)} \]

   4. associate-+r- 99.8%

      \[\leadsto x + \color{blue}{\left(\left(\left(-\left(y + 0.5\right) \cdot \log y\right) + y\right) - z\right)} \]

   5. *-commutative 99.8%

      \[\leadsto x + \left(\left(\left(-\color{blue}{\log y \cdot \left(y + 0.5\right)}\right) + y\right) - z\right) \]

   6. distribute-rgt-neg-in 99.8%

      \[\leadsto x + \left(\left(\color{blue}{\log y \cdot \left(-\left(y + 0.5\right)\right)} + y\right) - z\right) \]

   7. fma-define 99.9%

      \[\leadsto x + \left(\color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y\right)} - z\right) \]

   8. +-commutative 99.9%

      \[\leadsto x + \left(\mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y\right) - z\right) \]

   9. distribute-neg-in 99.9%

      \[\leadsto x + \left(\mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y\right) - z\right) \]

   10. unsub-neg 99.9%

       \[\leadsto x + \left(\mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y\right) - z\right) \]

   11. metadata-eval 99.9%

       \[\leadsto x + \left(\mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y\right) - z\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{x + \left(\mathsf{fma}\left(\log y, -0.5 - y, y\right) - z\right)} \]
4. Add Preprocessing

5. Final simplification 99.9%

   \[\leadsto x + \left(\mathsf{fma}\left(\log y, -0.5 - y, y\right) - z\right) \]
6. Add Preprocessing

Alternative 2: 88.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \log y\\ t_1 := \left(x - \log y \cdot 0.5\right) - z\\ \mathbf{if}\;y \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5000000000000:\\ \;\;\;\;y - \log y \cdot \left(y + 0.5\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{+149} \lor \neg \left(y \leq 2.85 \cdot 10^{+228}\right):\\ \;\;\;\;\left(y - t\_0\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (log y))) (t_1 (- (- x (* (log y) 0.5)) z)))
   (if (<= y 7.5e-7)
     t_1
     (if (<= y 5000000000000.0)
       (- y (* (log y) (+ y 0.5)))
       (if (<= y 6.8e+62)
         t_1
         (if (or (<= y 1.42e+149) (not (<= y 2.85e+228)))
           (- (- y t_0) z)
           (- (+ x y) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * log(y);
	double t_1 = (x - (log(y) * 0.5)) - z;
	double tmp;
	if (y <= 7.5e-7) {
		tmp = t_1;
	} else if (y <= 5000000000000.0) {
		tmp = y - (log(y) * (y + 0.5));
	} else if (y <= 6.8e+62) {
		tmp = t_1;
	} else if ((y <= 1.42e+149) || !(y <= 2.85e+228)) {
		tmp = (y - t_0) - z;
	} else {
		tmp = (x + y) - t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y * log(y)
    t_1 = (x - (log(y) * 0.5d0)) - z
    if (y <= 7.5d-7) then
        tmp = t_1
    else if (y <= 5000000000000.0d0) then
        tmp = y - (log(y) * (y + 0.5d0))
    else if (y <= 6.8d+62) then
        tmp = t_1
    else if ((y <= 1.42d+149) .or. (.not. (y <= 2.85d+228))) then
        tmp = (y - t_0) - z
    else
        tmp = (x + y) - t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * Math.log(y);
	double t_1 = (x - (Math.log(y) * 0.5)) - z;
	double tmp;
	if (y <= 7.5e-7) {
		tmp = t_1;
	} else if (y <= 5000000000000.0) {
		tmp = y - (Math.log(y) * (y + 0.5));
	} else if (y <= 6.8e+62) {
		tmp = t_1;
	} else if ((y <= 1.42e+149) || !(y <= 2.85e+228)) {
		tmp = (y - t_0) - z;
	} else {
		tmp = (x + y) - t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * math.log(y)
	t_1 = (x - (math.log(y) * 0.5)) - z
	tmp = 0
	if y <= 7.5e-7:
		tmp = t_1
	elif y <= 5000000000000.0:
		tmp = y - (math.log(y) * (y + 0.5))
	elif y <= 6.8e+62:
		tmp = t_1
	elif (y <= 1.42e+149) or not (y <= 2.85e+228):
		tmp = (y - t_0) - z
	else:
		tmp = (x + y) - t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * log(y))
	t_1 = Float64(Float64(x - Float64(log(y) * 0.5)) - z)
	tmp = 0.0
	if (y <= 7.5e-7)
		tmp = t_1;
	elseif (y <= 5000000000000.0)
		tmp = Float64(y - Float64(log(y) * Float64(y + 0.5)));
	elseif (y <= 6.8e+62)
		tmp = t_1;
	elseif ((y <= 1.42e+149) || !(y <= 2.85e+228))
		tmp = Float64(Float64(y - t_0) - z);
	else
		tmp = Float64(Float64(x + y) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * log(y);
	t_1 = (x - (log(y) * 0.5)) - z;
	tmp = 0.0;
	if (y <= 7.5e-7)
		tmp = t_1;
	elseif (y <= 5000000000000.0)
		tmp = y - (log(y) * (y + 0.5));
	elseif (y <= 6.8e+62)
		tmp = t_1;
	elseif ((y <= 1.42e+149) || ~((y <= 2.85e+228)))
		tmp = (y - t_0) - z;
	else
		tmp = (x + y) - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x - N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[y, 7.5e-7], t$95$1, If[LessEqual[y, 5000000000000.0], N[(y - N[(N[Log[y], $MachinePrecision] * N[(y + 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e+62], t$95$1, If[Or[LessEqual[y, 1.42e+149], N[Not[LessEqual[y, 2.85e+228]], $MachinePrecision]], N[(N[(y - t$95$0), $MachinePrecision] - z), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - t$95$0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < 7.5000000000000002e-7 or 5e12 < y < 6.80000000000000028e62

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 97.9%

      \[\leadsto \color{blue}{\left(x - 0.5 \cdot \log y\right)} - z \]
   4. Step-by-step derivation

      1. *-commutative 97.9%

         \[\leadsto \left(x - \color{blue}{\log y \cdot 0.5}\right) - z \]

   5. Simplified 97.9%

      \[\leadsto \color{blue}{\left(x - \log y \cdot 0.5\right)} - z \]

   if 7.5000000000000002e-7 < y < 5e12

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 99.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z} \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right) \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}} \]

      2. pow3 98.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right)}^{3}} \]

      3. sub-neg 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(\color{blue}{\left(x + \left(-\left(y + 0.5\right) \cdot \log y\right)\right)} + y\right) - z}\right)}^{3} \]

      4. associate-+l+ 98.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(x + \left(\left(-\left(y + 0.5\right) \cdot \log y\right) + y\right)\right)} - z}\right)}^{3} \]

      5. distribute-lft-neg-in 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-\left(y + 0.5\right)\right) \cdot \log y} + y\right)\right) - z}\right)}^{3} \]

      6. +-commutative 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(-\color{blue}{\left(0.5 + y\right)}\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      7. distribute-neg-in 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(\left(-0.5\right) + \left(-y\right)\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      8. metadata-eval 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(\color{blue}{-0.5} + \left(-y\right)\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      9. sub-neg 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-0.5 - y\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      10. *-commutative 98.9%

          \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\log y \cdot \left(-0.5 - y\right)} + y\right)\right) - z}\right)}^{3} \]

      11. fma-undefine 98.5%

          \[\leadsto {\left(\sqrt[3]{\left(x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)}\right) - z}\right)}^{3} \]

   4. Applied egg-rr 98.5%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x + \mathsf{fma}\left(\log y, -0.5 - y, y\right)\right) - z}\right)}^{3}} \]

   5. Taylor expanded in z around 0 100.0%

      \[\leadsto \color{blue}{x + \left(y + -1 \cdot \left(\log y \cdot \left(0.5 + y\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 100.0%

         \[\leadsto \color{blue}{\left(x + y\right) + -1 \cdot \left(\log y \cdot \left(0.5 + y\right)\right)} \]

      2. mul-1-neg 100.0%

         \[\leadsto \left(x + y\right) + \color{blue}{\left(-\log y \cdot \left(0.5 + y\right)\right)} \]

      3. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(x + y\right) - \log y \cdot \left(0.5 + y\right)} \]

      4. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(y + x\right)} - \log y \cdot \left(0.5 + y\right) \]

      5. +-commutative 100.0%

         \[\leadsto \left(y + x\right) - \log y \cdot \color{blue}{\left(y + 0.5\right)} \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{\left(y + x\right) - \log y \cdot \left(y + 0.5\right)} \]

   8. Taylor expanded in x around 0 87.6%

      \[\leadsto \color{blue}{y - \log y \cdot \left(0.5 + y\right)} \]

   if 6.80000000000000028e62 < y < 1.4200000000000001e149 or 2.8500000000000001e228 < y

   1. Initial program 99.6%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 91.4%

      \[\leadsto \left(\color{blue}{y \cdot \log \left(\frac{1}{y}\right)} + y\right) - z \]
   4. Step-by-step derivation

      1. *-commutative 91.4%

         \[\leadsto \left(\color{blue}{\log \left(\frac{1}{y}\right) \cdot y} + y\right) - z \]

      2. log-rec 91.4%

         \[\leadsto \left(\color{blue}{\left(-\log y\right)} \cdot y + y\right) - z \]

      3. distribute-lft-neg-in 91.4%

         \[\leadsto \left(\color{blue}{\left(-\log y \cdot y\right)} + y\right) - z \]

      4. distribute-rgt-neg-in 91.4%

         \[\leadsto \left(\color{blue}{\log y \cdot \left(-y\right)} + y\right) - z \]

   5. Simplified 91.4%

      \[\leadsto \left(\color{blue}{\log y \cdot \left(-y\right)} + y\right) - z \]
   6. Step-by-step derivation

      1. +-commutative 91.4%

         \[\leadsto \color{blue}{\left(y + \log y \cdot \left(-y\right)\right)} - z \]

      2. distribute-rgt-neg-out 91.4%

         \[\leadsto \left(y + \color{blue}{\left(-\log y \cdot y\right)}\right) - z \]

      3. unsub-neg 91.4%

         \[\leadsto \color{blue}{\left(y - \log y \cdot y\right)} - z \]

      4. add-sqr-sqrt 91.0%

         \[\leadsto \left(y - \log y \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}\right) - z \]

      5. sqrt-unprod 48.8%

         \[\leadsto \left(y - \log y \cdot \color{blue}{\sqrt{y \cdot y}}\right) - z \]

      6. sqr-neg 48.8%

         \[\leadsto \left(y - \log y \cdot \sqrt{\color{blue}{\left(-y\right) \cdot \left(-y\right)}}\right) - z \]

      7. sqrt-unprod 0.0%

         \[\leadsto \left(y - \log y \cdot \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)}\right) - z \]

      8. add-sqr-sqrt 18.7%

         \[\leadsto \left(y - \log y \cdot \color{blue}{\left(-y\right)}\right) - z \]

      9. *-commutative 18.7%

         \[\leadsto \left(y - \color{blue}{\left(-y\right) \cdot \log y}\right) - z \]

      10. add-sqr-sqrt 0.0%

          \[\leadsto \left(y - \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)} \cdot \log y\right) - z \]

      11. sqrt-unprod 48.8%

          \[\leadsto \left(y - \color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}} \cdot \log y\right) - z \]

      12. sqr-neg 48.8%

          \[\leadsto \left(y - \sqrt{\color{blue}{y \cdot y}} \cdot \log y\right) - z \]

      13. sqrt-unprod 91.0%

          \[\leadsto \left(y - \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} \cdot \log y\right) - z \]

      14. add-sqr-sqrt 91.4%

          \[\leadsto \left(y - \color{blue}{y} \cdot \log y\right) - z \]

   7. Applied egg-rr 91.4%

      \[\leadsto \color{blue}{\left(y - y \cdot \log y\right)} - z \]

   if 1.4200000000000001e149 < y < 2.8500000000000001e228

   1. Initial program 99.7%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 97.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z} \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right) \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}} \]

      2. pow3 97.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right)}^{3}} \]

      3. sub-neg 97.9%

         \[\leadsto {\left(\sqrt[3]{\left(\color{blue}{\left(x + \left(-\left(y + 0.5\right) \cdot \log y\right)\right)} + y\right) - z}\right)}^{3} \]

      4. associate-+l+ 97.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(x + \left(\left(-\left(y + 0.5\right) \cdot \log y\right) + y\right)\right)} - z}\right)}^{3} \]

      5. distribute-lft-neg-in 97.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-\left(y + 0.5\right)\right) \cdot \log y} + y\right)\right) - z}\right)}^{3} \]

      6. +-commutative 97.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(-\color{blue}{\left(0.5 + y\right)}\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      7. distribute-neg-in 97.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(\left(-0.5\right) + \left(-y\right)\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      8. metadata-eval 97.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(\color{blue}{-0.5} + \left(-y\right)\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      9. sub-neg 97.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-0.5 - y\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      10. *-commutative 97.9%

          \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\log y \cdot \left(-0.5 - y\right)} + y\right)\right) - z}\right)}^{3} \]

      11. fma-undefine 97.9%

          \[\leadsto {\left(\sqrt[3]{\left(x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)}\right) - z}\right)}^{3} \]

   4. Applied egg-rr 97.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x + \mathsf{fma}\left(\log y, -0.5 - y, y\right)\right) - z}\right)}^{3}} \]

   5. Taylor expanded in z around 0 89.4%

      \[\leadsto \color{blue}{x + \left(y + -1 \cdot \left(\log y \cdot \left(0.5 + y\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 89.4%

         \[\leadsto \color{blue}{\left(x + y\right) + -1 \cdot \left(\log y \cdot \left(0.5 + y\right)\right)} \]

      2. mul-1-neg 89.4%

         \[\leadsto \left(x + y\right) + \color{blue}{\left(-\log y \cdot \left(0.5 + y\right)\right)} \]

      3. sub-neg 89.4%

         \[\leadsto \color{blue}{\left(x + y\right) - \log y \cdot \left(0.5 + y\right)} \]

      4. +-commutative 89.4%

         \[\leadsto \color{blue}{\left(y + x\right)} - \log y \cdot \left(0.5 + y\right) \]

      5. +-commutative 89.4%

         \[\leadsto \left(y + x\right) - \log y \cdot \color{blue}{\left(y + 0.5\right)} \]

   7. Simplified 89.4%

      \[\leadsto \color{blue}{\left(y + x\right) - \log y \cdot \left(y + 0.5\right)} \]

   8. Taylor expanded in y around inf 89.4%

      \[\leadsto \left(y + x\right) - \color{blue}{-1 \cdot \left(y \cdot \log \left(\frac{1}{y}\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 89.4%

         \[\leadsto \left(y + x\right) - \color{blue}{\left(-y \cdot \log \left(\frac{1}{y}\right)\right)} \]

      2. log-rec 89.4%

         \[\leadsto \left(y + x\right) - \left(-y \cdot \color{blue}{\left(-\log y\right)}\right) \]

      3. distribute-rgt-neg-in 89.4%

         \[\leadsto \left(y + x\right) - \color{blue}{y \cdot \left(-\left(-\log y\right)\right)} \]

      4. remove-double-neg 89.4%

         \[\leadsto \left(y + x\right) - y \cdot \color{blue}{\log y} \]

   10. Simplified 89.4%

       \[\leadsto \left(y + x\right) - \color{blue}{y \cdot \log y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;\left(x - \log y \cdot 0.5\right) - z\\ \mathbf{elif}\;y \leq 5000000000000:\\ \;\;\;\;y - \log y \cdot \left(y + 0.5\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+62}:\\ \;\;\;\;\left(x - \log y \cdot 0.5\right) - z\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{+149} \lor \neg \left(y \leq 2.85 \cdot 10^{+228}\right):\\ \;\;\;\;\left(y - y \cdot \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;\left(x + y\right) - z\\ \mathbf{elif}\;y \leq 5000000000000:\\ \;\;\;\;y - \log y \cdot \left(y + 0.5\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+86}:\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \log y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 7.5e-7)
   (- (+ x y) z)
   (if (<= y 5000000000000.0)
     (- y (* (log y) (+ y 0.5)))
     (if (<= y 5.2e+86) (- x z) (- (+ x y) (* y (log y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 7.5e-7) {
		tmp = (x + y) - z;
	} else if (y <= 5000000000000.0) {
		tmp = y - (log(y) * (y + 0.5));
	} else if (y <= 5.2e+86) {
		tmp = x - z;
	} else {
		tmp = (x + y) - (y * log(y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 7.5d-7) then
        tmp = (x + y) - z
    else if (y <= 5000000000000.0d0) then
        tmp = y - (log(y) * (y + 0.5d0))
    else if (y <= 5.2d+86) then
        tmp = x - z
    else
        tmp = (x + y) - (y * log(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 7.5e-7) {
		tmp = (x + y) - z;
	} else if (y <= 5000000000000.0) {
		tmp = y - (Math.log(y) * (y + 0.5));
	} else if (y <= 5.2e+86) {
		tmp = x - z;
	} else {
		tmp = (x + y) - (y * Math.log(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 7.5e-7:
		tmp = (x + y) - z
	elif y <= 5000000000000.0:
		tmp = y - (math.log(y) * (y + 0.5))
	elif y <= 5.2e+86:
		tmp = x - z
	else:
		tmp = (x + y) - (y * math.log(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 7.5e-7)
		tmp = Float64(Float64(x + y) - z);
	elseif (y <= 5000000000000.0)
		tmp = Float64(y - Float64(log(y) * Float64(y + 0.5)));
	elseif (y <= 5.2e+86)
		tmp = Float64(x - z);
	else
		tmp = Float64(Float64(x + y) - Float64(y * log(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 7.5e-7)
		tmp = (x + y) - z;
	elseif (y <= 5000000000000.0)
		tmp = y - (log(y) * (y + 0.5));
	elseif (y <= 5.2e+86)
		tmp = x - z;
	else
		tmp = (x + y) - (y * log(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 7.5e-7], N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[y, 5000000000000.0], N[(y - N[(N[Log[y], $MachinePrecision] * N[(y + 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+86], N[(x - z), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < 7.5000000000000002e-7

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in x around -inf 99.9%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(x \cdot \left(\frac{\log y \cdot \left(0.5 + y\right)}{x} - 1\right)\right)} + y\right) - z \]
   4. Step-by-step derivation

      1. mul-1-neg 99.9%

         \[\leadsto \left(\color{blue}{\left(-x \cdot \left(\frac{\log y \cdot \left(0.5 + y\right)}{x} - 1\right)\right)} + y\right) - z \]

      2. sub-neg 99.9%

         \[\leadsto \left(\left(-x \cdot \color{blue}{\left(\frac{\log y \cdot \left(0.5 + y\right)}{x} + \left(-1\right)\right)}\right) + y\right) - z \]

      3. associate-/l* 99.9%

         \[\leadsto \left(\left(-x \cdot \left(\color{blue}{\log y \cdot \frac{0.5 + y}{x}} + \left(-1\right)\right)\right) + y\right) - z \]

      4. +-commutative 99.9%

         \[\leadsto \left(\left(-x \cdot \left(\log y \cdot \frac{\color{blue}{y + 0.5}}{x} + \left(-1\right)\right)\right) + y\right) - z \]

      5. metadata-eval 99.9%

         \[\leadsto \left(\left(-x \cdot \left(\log y \cdot \frac{y + 0.5}{x} + \color{blue}{-1}\right)\right) + y\right) - z \]

   5. Simplified 99.9%

      \[\leadsto \left(\color{blue}{\left(-x \cdot \left(\log y \cdot \frac{y + 0.5}{x} + -1\right)\right)} + y\right) - z \]

   6. Taylor expanded in x around inf 75.6%

      \[\leadsto \left(\left(-\color{blue}{-1 \cdot x}\right) + y\right) - z \]
   7. Step-by-step derivation

      1. neg-mul-1 75.6%

         \[\leadsto \left(\left(-\color{blue}{\left(-x\right)}\right) + y\right) - z \]

   8. Simplified 75.6%

      \[\leadsto \left(\left(-\color{blue}{\left(-x\right)}\right) + y\right) - z \]

   if 7.5000000000000002e-7 < y < 5e12

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 99.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z} \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right) \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}} \]

      2. pow3 98.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right)}^{3}} \]

      3. sub-neg 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(\color{blue}{\left(x + \left(-\left(y + 0.5\right) \cdot \log y\right)\right)} + y\right) - z}\right)}^{3} \]

      4. associate-+l+ 98.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(x + \left(\left(-\left(y + 0.5\right) \cdot \log y\right) + y\right)\right)} - z}\right)}^{3} \]

      5. distribute-lft-neg-in 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-\left(y + 0.5\right)\right) \cdot \log y} + y\right)\right) - z}\right)}^{3} \]

      6. +-commutative 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(-\color{blue}{\left(0.5 + y\right)}\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      7. distribute-neg-in 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(\left(-0.5\right) + \left(-y\right)\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      8. metadata-eval 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(\color{blue}{-0.5} + \left(-y\right)\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      9. sub-neg 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-0.5 - y\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      10. *-commutative 98.9%

          \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\log y \cdot \left(-0.5 - y\right)} + y\right)\right) - z}\right)}^{3} \]

      11. fma-undefine 98.5%

          \[\leadsto {\left(\sqrt[3]{\left(x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)}\right) - z}\right)}^{3} \]

   4. Applied egg-rr 98.5%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x + \mathsf{fma}\left(\log y, -0.5 - y, y\right)\right) - z}\right)}^{3}} \]

   5. Taylor expanded in z around 0 100.0%

      \[\leadsto \color{blue}{x + \left(y + -1 \cdot \left(\log y \cdot \left(0.5 + y\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 100.0%

         \[\leadsto \color{blue}{\left(x + y\right) + -1 \cdot \left(\log y \cdot \left(0.5 + y\right)\right)} \]

      2. mul-1-neg 100.0%

         \[\leadsto \left(x + y\right) + \color{blue}{\left(-\log y \cdot \left(0.5 + y\right)\right)} \]

      3. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(x + y\right) - \log y \cdot \left(0.5 + y\right)} \]

      4. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(y + x\right)} - \log y \cdot \left(0.5 + y\right) \]

      5. +-commutative 100.0%

         \[\leadsto \left(y + x\right) - \log y \cdot \color{blue}{\left(y + 0.5\right)} \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{\left(y + x\right) - \log y \cdot \left(y + 0.5\right)} \]

   8. Taylor expanded in x around 0 87.6%

      \[\leadsto \color{blue}{y - \log y \cdot \left(0.5 + y\right)} \]

   if 5e12 < y < 5.1999999999999995e86

   1. Initial program 99.8%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 73.6%

      \[\leadsto \color{blue}{x} - z \]

   if 5.1999999999999995e86 < y

   1. Initial program 99.6%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 98.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z} \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right) \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}} \]

      2. pow3 98.1%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right)}^{3}} \]

      3. sub-neg 98.1%

         \[\leadsto {\left(\sqrt[3]{\left(\color{blue}{\left(x + \left(-\left(y + 0.5\right) \cdot \log y\right)\right)} + y\right) - z}\right)}^{3} \]

      4. associate-+l+ 98.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(x + \left(\left(-\left(y + 0.5\right) \cdot \log y\right) + y\right)\right)} - z}\right)}^{3} \]

      5. distribute-lft-neg-in 98.1%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-\left(y + 0.5\right)\right) \cdot \log y} + y\right)\right) - z}\right)}^{3} \]

      6. +-commutative 98.1%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(-\color{blue}{\left(0.5 + y\right)}\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      7. distribute-neg-in 98.1%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(\left(-0.5\right) + \left(-y\right)\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      8. metadata-eval 98.1%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(\color{blue}{-0.5} + \left(-y\right)\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      9. sub-neg 98.1%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-0.5 - y\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      10. *-commutative 98.1%

          \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\log y \cdot \left(-0.5 - y\right)} + y\right)\right) - z}\right)}^{3} \]

      11. fma-undefine 98.1%

          \[\leadsto {\left(\sqrt[3]{\left(x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)}\right) - z}\right)}^{3} \]

   4. Applied egg-rr 98.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x + \mathsf{fma}\left(\log y, -0.5 - y, y\right)\right) - z}\right)}^{3}} \]

   5. Taylor expanded in z around 0 87.9%

      \[\leadsto \color{blue}{x + \left(y + -1 \cdot \left(\log y \cdot \left(0.5 + y\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 87.9%

         \[\leadsto \color{blue}{\left(x + y\right) + -1 \cdot \left(\log y \cdot \left(0.5 + y\right)\right)} \]

      2. mul-1-neg 87.9%

         \[\leadsto \left(x + y\right) + \color{blue}{\left(-\log y \cdot \left(0.5 + y\right)\right)} \]

      3. sub-neg 87.9%

         \[\leadsto \color{blue}{\left(x + y\right) - \log y \cdot \left(0.5 + y\right)} \]

      4. +-commutative 87.9%

         \[\leadsto \color{blue}{\left(y + x\right)} - \log y \cdot \left(0.5 + y\right) \]

      5. +-commutative 87.9%

         \[\leadsto \left(y + x\right) - \log y \cdot \color{blue}{\left(y + 0.5\right)} \]

   7. Simplified 87.9%

      \[\leadsto \color{blue}{\left(y + x\right) - \log y \cdot \left(y + 0.5\right)} \]

   8. Taylor expanded in y around inf 87.9%

      \[\leadsto \left(y + x\right) - \color{blue}{-1 \cdot \left(y \cdot \log \left(\frac{1}{y}\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 87.9%

         \[\leadsto \left(y + x\right) - \color{blue}{\left(-y \cdot \log \left(\frac{1}{y}\right)\right)} \]

      2. log-rec 87.9%

         \[\leadsto \left(y + x\right) - \left(-y \cdot \color{blue}{\left(-\log y\right)}\right) \]

      3. distribute-rgt-neg-in 87.9%

         \[\leadsto \left(y + x\right) - \color{blue}{y \cdot \left(-\left(-\log y\right)\right)} \]

      4. remove-double-neg 87.9%

         \[\leadsto \left(y + x\right) - y \cdot \color{blue}{\log y} \]

   10. Simplified 87.9%

       \[\leadsto \left(y + x\right) - \color{blue}{y \cdot \log y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;\left(x + y\right) - z\\ \mathbf{elif}\;y \leq 5000000000000:\\ \;\;\;\;y - \log y \cdot \left(y + 0.5\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+86}:\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - \log y \cdot 0.5\right) - z\\ \mathbf{if}\;y \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5000000000000:\\ \;\;\;\;y - \log y \cdot \left(y + 0.5\right)\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+86}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \log y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (- x (* (log y) 0.5)) z)))
   (if (<= y 7.5e-7)
     t_0
     (if (<= y 5000000000000.0)
       (- y (* (log y) (+ y 0.5)))
       (if (<= y 8.4e+86) t_0 (- (+ x y) (* y (log y))))))))

C

double code(double x, double y, double z) {
	double t_0 = (x - (log(y) * 0.5)) - z;
	double tmp;
	if (y <= 7.5e-7) {
		tmp = t_0;
	} else if (y <= 5000000000000.0) {
		tmp = y - (log(y) * (y + 0.5));
	} else if (y <= 8.4e+86) {
		tmp = t_0;
	} else {
		tmp = (x + y) - (y * log(y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x - (log(y) * 0.5d0)) - z
    if (y <= 7.5d-7) then
        tmp = t_0
    else if (y <= 5000000000000.0d0) then
        tmp = y - (log(y) * (y + 0.5d0))
    else if (y <= 8.4d+86) then
        tmp = t_0
    else
        tmp = (x + y) - (y * log(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x - (Math.log(y) * 0.5)) - z;
	double tmp;
	if (y <= 7.5e-7) {
		tmp = t_0;
	} else if (y <= 5000000000000.0) {
		tmp = y - (Math.log(y) * (y + 0.5));
	} else if (y <= 8.4e+86) {
		tmp = t_0;
	} else {
		tmp = (x + y) - (y * Math.log(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x - (math.log(y) * 0.5)) - z
	tmp = 0
	if y <= 7.5e-7:
		tmp = t_0
	elif y <= 5000000000000.0:
		tmp = y - (math.log(y) * (y + 0.5))
	elif y <= 8.4e+86:
		tmp = t_0
	else:
		tmp = (x + y) - (y * math.log(y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - Float64(log(y) * 0.5)) - z)
	tmp = 0.0
	if (y <= 7.5e-7)
		tmp = t_0;
	elseif (y <= 5000000000000.0)
		tmp = Float64(y - Float64(log(y) * Float64(y + 0.5)));
	elseif (y <= 8.4e+86)
		tmp = t_0;
	else
		tmp = Float64(Float64(x + y) - Float64(y * log(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x - (log(y) * 0.5)) - z;
	tmp = 0.0;
	if (y <= 7.5e-7)
		tmp = t_0;
	elseif (y <= 5000000000000.0)
		tmp = y - (log(y) * (y + 0.5));
	elseif (y <= 8.4e+86)
		tmp = t_0;
	else
		tmp = (x + y) - (y * log(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[y, 7.5e-7], t$95$0, If[LessEqual[y, 5000000000000.0], N[(y - N[(N[Log[y], $MachinePrecision] * N[(y + 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.4e+86], t$95$0, N[(N[(x + y), $MachinePrecision] - N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 7.5000000000000002e-7 or 5e12 < y < 8.3999999999999996e86

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 95.1%

      \[\leadsto \color{blue}{\left(x - 0.5 \cdot \log y\right)} - z \]
   4. Step-by-step derivation

      1. *-commutative 95.1%

         \[\leadsto \left(x - \color{blue}{\log y \cdot 0.5}\right) - z \]

   5. Simplified 95.1%

      \[\leadsto \color{blue}{\left(x - \log y \cdot 0.5\right)} - z \]

   if 7.5000000000000002e-7 < y < 5e12

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 99.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z} \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right) \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}} \]

      2. pow3 98.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right)}^{3}} \]

      3. sub-neg 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(\color{blue}{\left(x + \left(-\left(y + 0.5\right) \cdot \log y\right)\right)} + y\right) - z}\right)}^{3} \]

      4. associate-+l+ 98.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(x + \left(\left(-\left(y + 0.5\right) \cdot \log y\right) + y\right)\right)} - z}\right)}^{3} \]

      5. distribute-lft-neg-in 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-\left(y + 0.5\right)\right) \cdot \log y} + y\right)\right) - z}\right)}^{3} \]

      6. +-commutative 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(-\color{blue}{\left(0.5 + y\right)}\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      7. distribute-neg-in 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(\left(-0.5\right) + \left(-y\right)\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      8. metadata-eval 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(\color{blue}{-0.5} + \left(-y\right)\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      9. sub-neg 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-0.5 - y\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      10. *-commutative 98.9%

          \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\log y \cdot \left(-0.5 - y\right)} + y\right)\right) - z}\right)}^{3} \]

      11. fma-undefine 98.5%

          \[\leadsto {\left(\sqrt[3]{\left(x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)}\right) - z}\right)}^{3} \]

   4. Applied egg-rr 98.5%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x + \mathsf{fma}\left(\log y, -0.5 - y, y\right)\right) - z}\right)}^{3}} \]

   5. Taylor expanded in z around 0 100.0%

      \[\leadsto \color{blue}{x + \left(y + -1 \cdot \left(\log y \cdot \left(0.5 + y\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 100.0%

         \[\leadsto \color{blue}{\left(x + y\right) + -1 \cdot \left(\log y \cdot \left(0.5 + y\right)\right)} \]

      2. mul-1-neg 100.0%

         \[\leadsto \left(x + y\right) + \color{blue}{\left(-\log y \cdot \left(0.5 + y\right)\right)} \]

      3. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(x + y\right) - \log y \cdot \left(0.5 + y\right)} \]

      4. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(y + x\right)} - \log y \cdot \left(0.5 + y\right) \]

      5. +-commutative 100.0%

         \[\leadsto \left(y + x\right) - \log y \cdot \color{blue}{\left(y + 0.5\right)} \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{\left(y + x\right) - \log y \cdot \left(y + 0.5\right)} \]

   8. Taylor expanded in x around 0 87.6%

      \[\leadsto \color{blue}{y - \log y \cdot \left(0.5 + y\right)} \]

   if 8.3999999999999996e86 < y

   1. Initial program 99.6%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 98.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z} \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right) \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}} \]

      2. pow3 98.1%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right)}^{3}} \]

      3. sub-neg 98.1%

         \[\leadsto {\left(\sqrt[3]{\left(\color{blue}{\left(x + \left(-\left(y + 0.5\right) \cdot \log y\right)\right)} + y\right) - z}\right)}^{3} \]

      4. associate-+l+ 98.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(x + \left(\left(-\left(y + 0.5\right) \cdot \log y\right) + y\right)\right)} - z}\right)}^{3} \]

      5. distribute-lft-neg-in 98.1%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-\left(y + 0.5\right)\right) \cdot \log y} + y\right)\right) - z}\right)}^{3} \]

      6. +-commutative 98.1%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(-\color{blue}{\left(0.5 + y\right)}\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      7. distribute-neg-in 98.1%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(\left(-0.5\right) + \left(-y\right)\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      8. metadata-eval 98.1%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(\color{blue}{-0.5} + \left(-y\right)\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      9. sub-neg 98.1%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-0.5 - y\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      10. *-commutative 98.1%

          \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\log y \cdot \left(-0.5 - y\right)} + y\right)\right) - z}\right)}^{3} \]

      11. fma-undefine 98.1%

          \[\leadsto {\left(\sqrt[3]{\left(x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)}\right) - z}\right)}^{3} \]

   4. Applied egg-rr 98.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x + \mathsf{fma}\left(\log y, -0.5 - y, y\right)\right) - z}\right)}^{3}} \]

   5. Taylor expanded in z around 0 87.9%

      \[\leadsto \color{blue}{x + \left(y + -1 \cdot \left(\log y \cdot \left(0.5 + y\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 87.9%

         \[\leadsto \color{blue}{\left(x + y\right) + -1 \cdot \left(\log y \cdot \left(0.5 + y\right)\right)} \]

      2. mul-1-neg 87.9%

         \[\leadsto \left(x + y\right) + \color{blue}{\left(-\log y \cdot \left(0.5 + y\right)\right)} \]

      3. sub-neg 87.9%

         \[\leadsto \color{blue}{\left(x + y\right) - \log y \cdot \left(0.5 + y\right)} \]

      4. +-commutative 87.9%

         \[\leadsto \color{blue}{\left(y + x\right)} - \log y \cdot \left(0.5 + y\right) \]

      5. +-commutative 87.9%

         \[\leadsto \left(y + x\right) - \log y \cdot \color{blue}{\left(y + 0.5\right)} \]

   7. Simplified 87.9%

      \[\leadsto \color{blue}{\left(y + x\right) - \log y \cdot \left(y + 0.5\right)} \]

   8. Taylor expanded in y around inf 87.9%

      \[\leadsto \left(y + x\right) - \color{blue}{-1 \cdot \left(y \cdot \log \left(\frac{1}{y}\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 87.9%

         \[\leadsto \left(y + x\right) - \color{blue}{\left(-y \cdot \log \left(\frac{1}{y}\right)\right)} \]

      2. log-rec 87.9%

         \[\leadsto \left(y + x\right) - \left(-y \cdot \color{blue}{\left(-\log y\right)}\right) \]

      3. distribute-rgt-neg-in 87.9%

         \[\leadsto \left(y + x\right) - \color{blue}{y \cdot \left(-\left(-\log y\right)\right)} \]

      4. remove-double-neg 87.9%

         \[\leadsto \left(y + x\right) - y \cdot \color{blue}{\log y} \]

   10. Simplified 87.9%

       \[\leadsto \left(y + x\right) - \color{blue}{y \cdot \log y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;\left(x - \log y \cdot 0.5\right) - z\\ \mathbf{elif}\;y \leq 5000000000000:\\ \;\;\;\;y - \log y \cdot \left(y + 0.5\right)\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+86}:\\ \;\;\;\;\left(x - \log y \cdot 0.5\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;\left(x + y\right) - z\\ \mathbf{elif}\;y \leq 5000000000000:\\ \;\;\;\;y - \log y \cdot \left(y + 0.5\right)\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+108}:\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 7.5e-7)
   (- (+ x y) z)
   (if (<= y 5000000000000.0)
     (- y (* (log y) (+ y 0.5)))
     (if (<= y 1.06e+108) (- x z) (* y (- 1.0 (log y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 7.5e-7) {
		tmp = (x + y) - z;
	} else if (y <= 5000000000000.0) {
		tmp = y - (log(y) * (y + 0.5));
	} else if (y <= 1.06e+108) {
		tmp = x - z;
	} else {
		tmp = y * (1.0 - log(y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 7.5d-7) then
        tmp = (x + y) - z
    else if (y <= 5000000000000.0d0) then
        tmp = y - (log(y) * (y + 0.5d0))
    else if (y <= 1.06d+108) then
        tmp = x - z
    else
        tmp = y * (1.0d0 - log(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 7.5e-7) {
		tmp = (x + y) - z;
	} else if (y <= 5000000000000.0) {
		tmp = y - (Math.log(y) * (y + 0.5));
	} else if (y <= 1.06e+108) {
		tmp = x - z;
	} else {
		tmp = y * (1.0 - Math.log(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 7.5e-7:
		tmp = (x + y) - z
	elif y <= 5000000000000.0:
		tmp = y - (math.log(y) * (y + 0.5))
	elif y <= 1.06e+108:
		tmp = x - z
	else:
		tmp = y * (1.0 - math.log(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 7.5e-7)
		tmp = Float64(Float64(x + y) - z);
	elseif (y <= 5000000000000.0)
		tmp = Float64(y - Float64(log(y) * Float64(y + 0.5)));
	elseif (y <= 1.06e+108)
		tmp = Float64(x - z);
	else
		tmp = Float64(y * Float64(1.0 - log(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 7.5e-7)
		tmp = (x + y) - z;
	elseif (y <= 5000000000000.0)
		tmp = y - (log(y) * (y + 0.5));
	elseif (y <= 1.06e+108)
		tmp = x - z;
	else
		tmp = y * (1.0 - log(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 7.5e-7], N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[y, 5000000000000.0], N[(y - N[(N[Log[y], $MachinePrecision] * N[(y + 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.06e+108], N[(x - z), $MachinePrecision], N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < 7.5000000000000002e-7

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in x around -inf 99.9%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(x \cdot \left(\frac{\log y \cdot \left(0.5 + y\right)}{x} - 1\right)\right)} + y\right) - z \]
   4. Step-by-step derivation

      1. mul-1-neg 99.9%

         \[\leadsto \left(\color{blue}{\left(-x \cdot \left(\frac{\log y \cdot \left(0.5 + y\right)}{x} - 1\right)\right)} + y\right) - z \]

      2. sub-neg 99.9%

         \[\leadsto \left(\left(-x \cdot \color{blue}{\left(\frac{\log y \cdot \left(0.5 + y\right)}{x} + \left(-1\right)\right)}\right) + y\right) - z \]

      3. associate-/l* 99.9%

         \[\leadsto \left(\left(-x \cdot \left(\color{blue}{\log y \cdot \frac{0.5 + y}{x}} + \left(-1\right)\right)\right) + y\right) - z \]

      4. +-commutative 99.9%

         \[\leadsto \left(\left(-x \cdot \left(\log y \cdot \frac{\color{blue}{y + 0.5}}{x} + \left(-1\right)\right)\right) + y\right) - z \]

      5. metadata-eval 99.9%

         \[\leadsto \left(\left(-x \cdot \left(\log y \cdot \frac{y + 0.5}{x} + \color{blue}{-1}\right)\right) + y\right) - z \]

   5. Simplified 99.9%

      \[\leadsto \left(\color{blue}{\left(-x \cdot \left(\log y \cdot \frac{y + 0.5}{x} + -1\right)\right)} + y\right) - z \]

   6. Taylor expanded in x around inf 75.6%

      \[\leadsto \left(\left(-\color{blue}{-1 \cdot x}\right) + y\right) - z \]
   7. Step-by-step derivation

      1. neg-mul-1 75.6%

         \[\leadsto \left(\left(-\color{blue}{\left(-x\right)}\right) + y\right) - z \]

   8. Simplified 75.6%

      \[\leadsto \left(\left(-\color{blue}{\left(-x\right)}\right) + y\right) - z \]

   if 7.5000000000000002e-7 < y < 5e12

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 99.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z} \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right) \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}} \]

      2. pow3 98.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right)}^{3}} \]

      3. sub-neg 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(\color{blue}{\left(x + \left(-\left(y + 0.5\right) \cdot \log y\right)\right)} + y\right) - z}\right)}^{3} \]

      4. associate-+l+ 98.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(x + \left(\left(-\left(y + 0.5\right) \cdot \log y\right) + y\right)\right)} - z}\right)}^{3} \]

      5. distribute-lft-neg-in 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-\left(y + 0.5\right)\right) \cdot \log y} + y\right)\right) - z}\right)}^{3} \]

      6. +-commutative 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(-\color{blue}{\left(0.5 + y\right)}\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      7. distribute-neg-in 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(\left(-0.5\right) + \left(-y\right)\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      8. metadata-eval 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(\color{blue}{-0.5} + \left(-y\right)\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      9. sub-neg 98.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-0.5 - y\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      10. *-commutative 98.9%

          \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\log y \cdot \left(-0.5 - y\right)} + y\right)\right) - z}\right)}^{3} \]

      11. fma-undefine 98.5%

          \[\leadsto {\left(\sqrt[3]{\left(x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)}\right) - z}\right)}^{3} \]

   4. Applied egg-rr 98.5%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x + \mathsf{fma}\left(\log y, -0.5 - y, y\right)\right) - z}\right)}^{3}} \]

   5. Taylor expanded in z around 0 100.0%

      \[\leadsto \color{blue}{x + \left(y + -1 \cdot \left(\log y \cdot \left(0.5 + y\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 100.0%

         \[\leadsto \color{blue}{\left(x + y\right) + -1 \cdot \left(\log y \cdot \left(0.5 + y\right)\right)} \]

      2. mul-1-neg 100.0%

         \[\leadsto \left(x + y\right) + \color{blue}{\left(-\log y \cdot \left(0.5 + y\right)\right)} \]

      3. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(x + y\right) - \log y \cdot \left(0.5 + y\right)} \]

      4. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(y + x\right)} - \log y \cdot \left(0.5 + y\right) \]

      5. +-commutative 100.0%

         \[\leadsto \left(y + x\right) - \log y \cdot \color{blue}{\left(y + 0.5\right)} \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{\left(y + x\right) - \log y \cdot \left(y + 0.5\right)} \]

   8. Taylor expanded in x around 0 87.6%

      \[\leadsto \color{blue}{y - \log y \cdot \left(0.5 + y\right)} \]

   if 5e12 < y < 1.06e108

   1. Initial program 99.8%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 73.3%

      \[\leadsto \color{blue}{x} - z \]

   if 1.06e108 < y

   1. Initial program 99.6%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 98.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z} \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right) \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}} \]

      2. pow3 98.2%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right)}^{3}} \]

      3. sub-neg 98.2%

         \[\leadsto {\left(\sqrt[3]{\left(\color{blue}{\left(x + \left(-\left(y + 0.5\right) \cdot \log y\right)\right)} + y\right) - z}\right)}^{3} \]

      4. associate-+l+ 98.2%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(x + \left(\left(-\left(y + 0.5\right) \cdot \log y\right) + y\right)\right)} - z}\right)}^{3} \]

      5. distribute-lft-neg-in 98.2%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-\left(y + 0.5\right)\right) \cdot \log y} + y\right)\right) - z}\right)}^{3} \]

      6. +-commutative 98.2%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(-\color{blue}{\left(0.5 + y\right)}\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      7. distribute-neg-in 98.2%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(\left(-0.5\right) + \left(-y\right)\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      8. metadata-eval 98.2%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(\color{blue}{-0.5} + \left(-y\right)\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      9. sub-neg 98.2%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-0.5 - y\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      10. *-commutative 98.2%

          \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\log y \cdot \left(-0.5 - y\right)} + y\right)\right) - z}\right)}^{3} \]

      11. fma-undefine 98.1%

          \[\leadsto {\left(\sqrt[3]{\left(x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)}\right) - z}\right)}^{3} \]

   4. Applied egg-rr 98.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x + \mathsf{fma}\left(\log y, -0.5 - y, y\right)\right) - z}\right)}^{3}} \]

   5. Taylor expanded in y around inf 77.0%

      \[\leadsto \color{blue}{y \cdot \left(1 + \log \left(\frac{1}{y}\right)\right)} \]
   6. Step-by-step derivation

      1. log-rec 77.0%

         \[\leadsto y \cdot \left(1 + \color{blue}{\left(-\log y\right)}\right) \]

      2. neg-mul-1 77.0%

         \[\leadsto y \cdot \left(1 + \color{blue}{-1 \cdot \log y}\right) \]

      3. neg-mul-1 77.0%

         \[\leadsto y \cdot \left(1 + \color{blue}{\left(-\log y\right)}\right) \]

      4. sub-neg 77.0%

         \[\leadsto y \cdot \color{blue}{\left(1 - \log y\right)} \]

   7. Simplified 77.0%

      \[\leadsto \color{blue}{y \cdot \left(1 - \log y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;\left(x + y\right) - z\\ \mathbf{elif}\;y \leq 5000000000000:\\ \;\;\;\;y - \log y \cdot \left(y + 0.5\right)\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+108}:\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.2:\\ \;\;\;\;\left(x - \log y \cdot 0.5\right) - z\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(1 - \log y\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 3.2) (- (- x (* (log y) 0.5)) z) (+ x (- (* y (- 1.0 (log y))) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.2) {
		tmp = (x - (log(y) * 0.5)) - z;
	} else {
		tmp = x + ((y * (1.0 - log(y))) - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 3.2d0) then
        tmp = (x - (log(y) * 0.5d0)) - z
    else
        tmp = x + ((y * (1.0d0 - log(y))) - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.2) {
		tmp = (x - (Math.log(y) * 0.5)) - z;
	} else {
		tmp = x + ((y * (1.0 - Math.log(y))) - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 3.2:
		tmp = (x - (math.log(y) * 0.5)) - z
	else:
		tmp = x + ((y * (1.0 - math.log(y))) - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 3.2)
		tmp = Float64(Float64(x - Float64(log(y) * 0.5)) - z);
	else
		tmp = Float64(x + Float64(Float64(y * Float64(1.0 - log(y))) - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 3.2)
		tmp = (x - (log(y) * 0.5)) - z;
	else
		tmp = x + ((y * (1.0 - log(y))) - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 3.2], N[(N[(x - N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(x + N[(N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.2000000000000002

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 98.6%

      \[\leadsto \color{blue}{\left(x - 0.5 \cdot \log y\right)} - z \]
   4. Step-by-step derivation

      1. *-commutative 98.6%

         \[\leadsto \left(x - \color{blue}{\log y \cdot 0.5}\right) - z \]

   5. Simplified 98.6%

      \[\leadsto \color{blue}{\left(x - \log y \cdot 0.5\right)} - z \]

   if 3.2000000000000002 < y

   1. Initial program 99.7%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 99.6%

         \[\leadsto \color{blue}{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)} \]

      2. sub-neg 99.6%

         \[\leadsto \color{blue}{\left(x + \left(-\left(y + 0.5\right) \cdot \log y\right)\right)} + \left(y - z\right) \]

      3. associate-+l+ 99.6%

         \[\leadsto \color{blue}{x + \left(\left(-\left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)\right)} \]

      4. associate-+r- 99.7%

         \[\leadsto x + \color{blue}{\left(\left(\left(-\left(y + 0.5\right) \cdot \log y\right) + y\right) - z\right)} \]

      5. *-commutative 99.7%

         \[\leadsto x + \left(\left(\left(-\color{blue}{\log y \cdot \left(y + 0.5\right)}\right) + y\right) - z\right) \]

      6. distribute-rgt-neg-in 99.7%

         \[\leadsto x + \left(\left(\color{blue}{\log y \cdot \left(-\left(y + 0.5\right)\right)} + y\right) - z\right) \]

      7. fma-define 99.8%

         \[\leadsto x + \left(\color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y\right)} - z\right) \]

      8. +-commutative 99.8%

         \[\leadsto x + \left(\mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y\right) - z\right) \]

      9. distribute-neg-in 99.8%

         \[\leadsto x + \left(\mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y\right) - z\right) \]

      10. unsub-neg 99.8%

          \[\leadsto x + \left(\mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y\right) - z\right) \]

      11. metadata-eval 99.8%

          \[\leadsto x + \left(\mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y\right) - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\mathsf{fma}\left(\log y, -0.5 - y, y\right) - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 98.3%

      \[\leadsto x + \left(\color{blue}{y \cdot \left(1 + \log \left(\frac{1}{y}\right)\right)} - z\right) \]
   6. Step-by-step derivation

      1. log-rec 98.3%

         \[\leadsto x + \left(y \cdot \left(1 + \color{blue}{\left(-\log y\right)}\right) - z\right) \]

      2. sub-neg 98.3%

         \[\leadsto x + \left(y \cdot \color{blue}{\left(1 - \log y\right)} - z\right) \]

   7. Simplified 98.3%

      \[\leadsto x + \left(\color{blue}{y \cdot \left(1 - \log y\right)} - z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.2:\\ \;\;\;\;\left(x - \log y \cdot 0.5\right) - z\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(1 - \log y\right) - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(y - \left(\log y \cdot \left(y + 0.5\right) - x\right)\right) - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (- y (- (* (log y) (+ y 0.5)) x)) z))

C

double code(double x, double y, double z) {
	return (y - ((log(y) * (y + 0.5)) - x)) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (y - ((log(y) * (y + 0.5d0)) - x)) - z
end function

Java

public static double code(double x, double y, double z) {
	return (y - ((Math.log(y) * (y + 0.5)) - x)) - z;
}

Python

def code(x, y, z):
	return (y - ((math.log(y) * (y + 0.5)) - x)) - z

Julia

function code(x, y, z)
	return Float64(Float64(y - Float64(Float64(log(y) * Float64(y + 0.5)) - x)) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (y - ((log(y) * (y + 0.5)) - x)) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(y - N[(N[(N[Log[y], $MachinePrecision] * N[(y + 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
2. Add Preprocessing

3. Final simplification 99.8%

   \[\leadsto \left(y - \left(\log y \cdot \left(y + 0.5\right) - x\right)\right) - z \]
4. Add Preprocessing

Alternative 8: 72.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.15 \cdot 10^{+108}:\\ \;\;\;\;\left(x + y\right) - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.15e+108) (- (+ x y) z) (* y (- 1.0 (log y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.15e+108) {
		tmp = (x + y) - z;
	} else {
		tmp = y * (1.0 - log(y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 2.15d+108) then
        tmp = (x + y) - z
    else
        tmp = y * (1.0d0 - log(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.15e+108) {
		tmp = (x + y) - z;
	} else {
		tmp = y * (1.0 - Math.log(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.15e+108:
		tmp = (x + y) - z
	else:
		tmp = y * (1.0 - math.log(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.15e+108)
		tmp = Float64(Float64(x + y) - z);
	else
		tmp = Float64(y * Float64(1.0 - log(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.15e+108)
		tmp = (x + y) - z;
	else
		tmp = y * (1.0 - log(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.15e+108], N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision], N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.14999999999999998e108

   1. Initial program 99.9%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in x around -inf 96.7%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(x \cdot \left(\frac{\log y \cdot \left(0.5 + y\right)}{x} - 1\right)\right)} + y\right) - z \]
   4. Step-by-step derivation

      1. mul-1-neg 96.7%

         \[\leadsto \left(\color{blue}{\left(-x \cdot \left(\frac{\log y \cdot \left(0.5 + y\right)}{x} - 1\right)\right)} + y\right) - z \]

      2. sub-neg 96.7%

         \[\leadsto \left(\left(-x \cdot \color{blue}{\left(\frac{\log y \cdot \left(0.5 + y\right)}{x} + \left(-1\right)\right)}\right) + y\right) - z \]

      3. associate-/l* 96.7%

         \[\leadsto \left(\left(-x \cdot \left(\color{blue}{\log y \cdot \frac{0.5 + y}{x}} + \left(-1\right)\right)\right) + y\right) - z \]

      4. +-commutative 96.7%

         \[\leadsto \left(\left(-x \cdot \left(\log y \cdot \frac{\color{blue}{y + 0.5}}{x} + \left(-1\right)\right)\right) + y\right) - z \]

      5. metadata-eval 96.7%

         \[\leadsto \left(\left(-x \cdot \left(\log y \cdot \frac{y + 0.5}{x} + \color{blue}{-1}\right)\right) + y\right) - z \]

   5. Simplified 96.7%

      \[\leadsto \left(\color{blue}{\left(-x \cdot \left(\log y \cdot \frac{y + 0.5}{x} + -1\right)\right)} + y\right) - z \]

   6. Taylor expanded in x around inf 72.3%

      \[\leadsto \left(\left(-\color{blue}{-1 \cdot x}\right) + y\right) - z \]
   7. Step-by-step derivation

      1. neg-mul-1 72.3%

         \[\leadsto \left(\left(-\color{blue}{\left(-x\right)}\right) + y\right) - z \]

   8. Simplified 72.3%

      \[\leadsto \left(\left(-\color{blue}{\left(-x\right)}\right) + y\right) - z \]

   if 2.14999999999999998e108 < y

   1. Initial program 99.6%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 98.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z} \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right) \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}} \]

      2. pow3 98.2%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right)}^{3}} \]

      3. sub-neg 98.2%

         \[\leadsto {\left(\sqrt[3]{\left(\color{blue}{\left(x + \left(-\left(y + 0.5\right) \cdot \log y\right)\right)} + y\right) - z}\right)}^{3} \]

      4. associate-+l+ 98.2%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(x + \left(\left(-\left(y + 0.5\right) \cdot \log y\right) + y\right)\right)} - z}\right)}^{3} \]

      5. distribute-lft-neg-in 98.2%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-\left(y + 0.5\right)\right) \cdot \log y} + y\right)\right) - z}\right)}^{3} \]

      6. +-commutative 98.2%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(-\color{blue}{\left(0.5 + y\right)}\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      7. distribute-neg-in 98.2%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(\left(-0.5\right) + \left(-y\right)\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      8. metadata-eval 98.2%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(\color{blue}{-0.5} + \left(-y\right)\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      9. sub-neg 98.2%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-0.5 - y\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      10. *-commutative 98.2%

          \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\log y \cdot \left(-0.5 - y\right)} + y\right)\right) - z}\right)}^{3} \]

      11. fma-undefine 98.1%

          \[\leadsto {\left(\sqrt[3]{\left(x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)}\right) - z}\right)}^{3} \]

   4. Applied egg-rr 98.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x + \mathsf{fma}\left(\log y, -0.5 - y, y\right)\right) - z}\right)}^{3}} \]

   5. Taylor expanded in y around inf 77.0%

      \[\leadsto \color{blue}{y \cdot \left(1 + \log \left(\frac{1}{y}\right)\right)} \]
   6. Step-by-step derivation

      1. log-rec 77.0%

         \[\leadsto y \cdot \left(1 + \color{blue}{\left(-\log y\right)}\right) \]

      2. neg-mul-1 77.0%

         \[\leadsto y \cdot \left(1 + \color{blue}{-1 \cdot \log y}\right) \]

      3. neg-mul-1 77.0%

         \[\leadsto y \cdot \left(1 + \color{blue}{\left(-\log y\right)}\right) \]

      4. sub-neg 77.0%

         \[\leadsto y \cdot \color{blue}{\left(1 - \log y\right)} \]

   7. Simplified 77.0%

      \[\leadsto \color{blue}{y \cdot \left(1 - \log y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.15 \cdot 10^{+108}:\\ \;\;\;\;\left(x + y\right) - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.3% accurate, 9.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+31}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.3e+48) x (if (<= x 5.2e+31) (- z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.3e+48) {
		tmp = x;
	} else if (x <= 5.2e+31) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.3d+48)) then
        tmp = x
    else if (x <= 5.2d+31) then
        tmp = -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.3e+48) {
		tmp = x;
	} else if (x <= 5.2e+31) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.3e+48:
		tmp = x
	elif x <= 5.2e+31:
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.3e+48)
		tmp = x;
	elseif (x <= 5.2e+31)
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.3e+48)
		tmp = x;
	elseif (x <= 5.2e+31)
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.3e+48], x, If[LessEqual[x, 5.2e+31], (-z), x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.29999999999999998e48 or 5.2e31 < x

   1. Initial program 99.9%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 98.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z} \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right) \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}} \]

      2. pow3 97.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right)}^{3}} \]

      3. sub-neg 97.9%

         \[\leadsto {\left(\sqrt[3]{\left(\color{blue}{\left(x + \left(-\left(y + 0.5\right) \cdot \log y\right)\right)} + y\right) - z}\right)}^{3} \]

      4. associate-+l+ 97.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(x + \left(\left(-\left(y + 0.5\right) \cdot \log y\right) + y\right)\right)} - z}\right)}^{3} \]

      5. distribute-lft-neg-in 97.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-\left(y + 0.5\right)\right) \cdot \log y} + y\right)\right) - z}\right)}^{3} \]

      6. +-commutative 97.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(-\color{blue}{\left(0.5 + y\right)}\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      7. distribute-neg-in 97.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(\left(-0.5\right) + \left(-y\right)\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      8. metadata-eval 97.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(\color{blue}{-0.5} + \left(-y\right)\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      9. sub-neg 97.9%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-0.5 - y\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      10. *-commutative 97.9%

          \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\log y \cdot \left(-0.5 - y\right)} + y\right)\right) - z}\right)}^{3} \]

      11. fma-undefine 97.9%

          \[\leadsto {\left(\sqrt[3]{\left(x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)}\right) - z}\right)}^{3} \]

   4. Applied egg-rr 97.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x + \mathsf{fma}\left(\log y, -0.5 - y, y\right)\right) - z}\right)}^{3}} \]

   5. Taylor expanded in x around inf 71.3%

      \[\leadsto \color{blue}{x} \]

   if -1.29999999999999998e48 < x < 5.2e31

   1. Initial program 99.8%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 97.9%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z} \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right) \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}} \]

      2. pow3 98.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right)}^{3}} \]

      3. sub-neg 98.0%

         \[\leadsto {\left(\sqrt[3]{\left(\color{blue}{\left(x + \left(-\left(y + 0.5\right) \cdot \log y\right)\right)} + y\right) - z}\right)}^{3} \]

      4. associate-+l+ 98.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(x + \left(\left(-\left(y + 0.5\right) \cdot \log y\right) + y\right)\right)} - z}\right)}^{3} \]

      5. distribute-lft-neg-in 98.0%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-\left(y + 0.5\right)\right) \cdot \log y} + y\right)\right) - z}\right)}^{3} \]

      6. +-commutative 98.0%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(-\color{blue}{\left(0.5 + y\right)}\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      7. distribute-neg-in 98.0%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(\left(-0.5\right) + \left(-y\right)\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      8. metadata-eval 98.0%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(\color{blue}{-0.5} + \left(-y\right)\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      9. sub-neg 98.0%

         \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-0.5 - y\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

      10. *-commutative 98.0%

          \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\log y \cdot \left(-0.5 - y\right)} + y\right)\right) - z}\right)}^{3} \]

      11. fma-undefine 98.0%

          \[\leadsto {\left(\sqrt[3]{\left(x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)}\right) - z}\right)}^{3} \]

   4. Applied egg-rr 98.0%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x + \mathsf{fma}\left(\log y, -0.5 - y, y\right)\right) - z}\right)}^{3}} \]

   5. Taylor expanded in z around inf 39.3%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   6. Step-by-step derivation

      1. neg-mul-1 39.3%

         \[\leadsto \color{blue}{-z} \]

   7. Simplified 39.3%

      \[\leadsto \color{blue}{-z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+31}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.4% accurate, 37.0× speedup

Math

\[\begin{array}{l} \\ x - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x z))

C

double code(double x, double y, double z) {
	return x - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x - z
end function

Java

public static double code(double x, double y, double z) {
	return x - z;
}

Python

def code(x, y, z):
	return x - z

Julia

function code(x, y, z)
	return Float64(x - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - z;
end

Wolfram

code[x_, y_, z_] := N[(x - z), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
2. Add Preprocessing

3. Taylor expanded in x around inf 57.3%

   \[\leadsto \color{blue}{x} - z \]

4. Final simplification 57.3%

   \[\leadsto x - z \]
5. Add Preprocessing

Alternative 11: 30.8% accurate, 111.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
2. Add Preprocessing
3. Step-by-step derivation

   1. add-cube-cbrt 98.0%

      \[\leadsto \color{blue}{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z} \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right) \cdot \sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}} \]

   2. pow3 98.0%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z}\right)}^{3}} \]

   3. sub-neg 98.0%

      \[\leadsto {\left(\sqrt[3]{\left(\color{blue}{\left(x + \left(-\left(y + 0.5\right) \cdot \log y\right)\right)} + y\right) - z}\right)}^{3} \]

   4. associate-+l+ 98.0%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(x + \left(\left(-\left(y + 0.5\right) \cdot \log y\right) + y\right)\right)} - z}\right)}^{3} \]

   5. distribute-lft-neg-in 98.0%

      \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-\left(y + 0.5\right)\right) \cdot \log y} + y\right)\right) - z}\right)}^{3} \]

   6. +-commutative 98.0%

      \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(-\color{blue}{\left(0.5 + y\right)}\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

   7. distribute-neg-in 98.0%

      \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(\left(-0.5\right) + \left(-y\right)\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

   8. metadata-eval 98.0%

      \[\leadsto {\left(\sqrt[3]{\left(x + \left(\left(\color{blue}{-0.5} + \left(-y\right)\right) \cdot \log y + y\right)\right) - z}\right)}^{3} \]

   9. sub-neg 98.0%

      \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\left(-0.5 - y\right)} \cdot \log y + y\right)\right) - z}\right)}^{3} \]

   10. *-commutative 98.0%

       \[\leadsto {\left(\sqrt[3]{\left(x + \left(\color{blue}{\log y \cdot \left(-0.5 - y\right)} + y\right)\right) - z}\right)}^{3} \]

   11. fma-undefine 97.9%

       \[\leadsto {\left(\sqrt[3]{\left(x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)}\right) - z}\right)}^{3} \]

4. Applied egg-rr 97.9%

   \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x + \mathsf{fma}\left(\log y, -0.5 - y, y\right)\right) - z}\right)}^{3}} \]

5. Taylor expanded in x around inf 32.8%

   \[\leadsto \color{blue}{x} \]

6. Final simplification 32.8%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(y + x\right) - z\right) - \left(y + 0.5\right) \cdot \log y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (- (+ y x) z) (* (+ y 0.5) (log y))))

C

double code(double x, double y, double z) {
	return ((y + x) - z) - ((y + 0.5) * log(y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((y + x) - z) - ((y + 0.5d0) * log(y))
end function

Java

public static double code(double x, double y, double z) {
	return ((y + x) - z) - ((y + 0.5) * Math.log(y));
}

Python

def code(x, y, z):
	return ((y + x) - z) - ((y + 0.5) * math.log(y))

Julia

function code(x, y, z)
	return Float64(Float64(Float64(y + x) - z) - Float64(Float64(y + 0.5) * log(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((y + x) - z) - ((y + 0.5) * log(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(y + x), $MachinePrecision] - z), $MachinePrecision] - N[(N[(y + 0.5), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024059 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (- (- (+ y x) z) (* (+ y 0.5) (log y)))

  (- (+ (- x (* (+ y 0.5) (log y))) y) z))